Rubik's cube and held it by two diagonally opposite vertices and rotated it till it reached the same position, by how many degrees did it take a turn?

Is this just 360 degrees?

It depends what you mean by "the same position". If you want each of the constituent cubelets in the Rubik's cube to return to its original position then the answer will be 360º. If you just want the cube as a whole to occupy the same space as originally then 120º is the answer.